Problem: Simplify the following expression: $y = \dfrac{-5r^2 + 30r + 135}{r + 3} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-5$ , so we can rewrite the expression: $ y =\dfrac{-5(r^2 - 6r - 27)}{r + 3} $ Then we factor the remaining polynomial: $r^2 {-6}r {-27} $ ${3} {-9} = {-6}$ ${3} \times {-9} = {-27}$ $ (r + {3}) (r {-9}) $ This gives us a factored expression: $\dfrac{-5(r + {3}) (r {-9})}{r + 3}$ We can divide the numerator and denominator by $(r - 3)$ on condition that $r \neq -3$ Therefore $y = -5(r - 9); r \neq -3$